Quandaries and Queries


does anyone have a formula for calculating the length of an arc if I have the circle radius and the cord length of the arc??





Hi Gavin,

If M is the midpoint of the chord as in the diagram then PCM is a right triangle. Hence the angle PCM has sine |MP|/|PC|.

Since you know the radius |PC|, and |MP| is half the chord length, you can find sin(anglePCM). Use the inverse sine function to find this angle in radians and then double it to find the angle PCQ.

The length of the arc is given by

a = r theta where r is the radius of the circle and theta is the angle (here the angle PCQ) measured in radians.

I hope this helps,

Go to Math Central